A Not So Impossible Machine Based on the GHZ Paradox

Brian R. La Cour

David Thomas Pegg

The retrocausality inherent in the retrodictive description of a quantum optical device called the quantum scissors allows this device to be used as a non-deterministic time machine. We show how the device can be used to model the time travel paradox of retrospective suicide. Here a man goes back in time and interferes with his own birth, weakening his infant self in such a way that he is killed by the time machine and is unable to interfere with his own birth. We find that the paradox is avoided by interfering quantum mechanical amplitudes making the time travel event impossible in this case. A slight modification that limits the interference with the birth so that the infant is only injured by the time machine to give a self-consistent cycle does, however, render the time travel event possible. This lends support to the idea that time travel is only possible if it yields a self-consistent cycle that avoids a paradox.

Peter Michael Kogge

Ian Richard C Buckley

Monogamy of entanglement states that quantum correlations cannot be freely shared: if two parties are maximally entangled, neither can be entangled with a third. The Fano plane $\mathrm{PG}(2,2)$ appears to violate this principle — its Hamiltonian ground state simultaneously correlates all seven directed triples. Hardy's paradox is a complementary phenomenon: four conditions on a multi-qubit state force the classically impossible conclusion $P(Z_+,\ldots,Z_+) = 0$, yet quantum mechanics permits $P(Z_+,\ldots,Z_+) > 0$. Both are well-understood within standard quantum mechanics; neither was ever mysterious to quantum theory itself. This paper identifies a single necessary condition that unifies both phenomena: irreducible three-body entanglement, as measured by the Coffman–Kundu–Wootters three-tangle $\tau_3$. The Fano monogamy apparent paradox dissolves once one observes that $C(i,j) < 1$ for all pairs and $\tau_3 > 0$ for Fano-line triples — the correlations are triangular, not pairwise. For the tripartite Hardy impossible event ($N=3$), we show numerically that $\tau_3 > 0$ is a necessary condition: no W-class or product state ($\tau_3 = 0$) satisfies all four Hardy conditions simultaneously, confirmed across 54 independent free-state optimisations (JAX/Adam, A100 GPU). The open question — whether this is provable algebraically — is stated explicitly. The novel contribution is the connection between the Dür–Vidal–Cirac entanglement classification and Hardy-type nonlocality: GHZ-class states ($\tau_3 > 0$) can exhibit the tripartite impossible event; W-class states cannot. Within the Adelic Simplicial Architecture (ASA), both phenomena share a further geometric explanation: the octonion associator $|\mathcal{A}(e_i,e_j,e_k)| = 0$ on Fano-line triples and $|\mathcal{A}| = 2$ elsewhere is the algebraic signature of the same triangular irreducibility, connecting the monogamy resolution and the Hardy condition to the associator firewall of the companion papers on the Spacelike Associator Paradox and Hardy's Paradox and the Fano Associator.

Vasil Penchev

Quantum computer is considered as a generalization of Turing machine. The bits are substituted by qubits. In turn, a "qubit" is the generalization of "bit" referring to infinite sets or series. It extends the consept of calculation from finite processes and algorithms to infinite ones, impossible as to any Turing machines (such as our computers). However, the concept of quantum computer mets all paradoxes of infinity such as Gödel's incompletness theorems (1931), etc. A philosophical reflection on how quantum computer might implement the idea of "infinite calculation" is the main subject.